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The article is concerned with discovery and development of the particular mathematics behind the Standard Model. This has nothing to do with human behavior, which is what is referred to when citing the Laws of Nature.[1] They meant, instead, the Laws of Physics, which more often than not aren't really laws, but theories instead.

[1] https://en.wikipedia.org/wiki/Natural_law

The Stanford Encyclopedia of Philosophy would disagree: it has an article entitled "Laws of Nature" (https://plato.stanford.edu/entries/laws-of-nature/) and separate articles on "Natural Law Theories" (https://plato.stanford.edu/entries/natural-law-theories/) and on "The Natural Law Tradition in Ethics" (https://plato.stanford.edu/entries/natural-law-ethics/). The disagreement over the term "Laws of Nature" apparently goes back at least to Hobbes and Boyle (https://plato.stanford.edu/entries/hobbes-science/#HobbExpeC...).
I would very strongly guess that, these days, around these American english-speaking parts, the idiomatic definitions, i.e. contrary to acceptable or moral behavior, or impossible seeming or unlikely circumstances, e.g. "murder goes against the laws of nature," also "surviving a plane crash defies the laws of nature," are perhaps exponentially more popular, because a percentage of song lyrical hooks will often describe examples of this use of the phrase, what goes up must come down, and so on and so forth, but I must concede I was unaware of its use conversely in the literal sense. But I don't get out much and feel I have read enough boring stuff, more so, I feel a little victimized for probably wasting significant portions of the best years of my life reading material concerned with boring topics by dedicated and qualified but excessively boring writers. There are exceptions, of course, the usual suspects, the great writers.
I recommend following the link in the article to her videos. There are 14 of them in all and they build the basis for the relationships that she has developed between quaternions and octonions and describe how to relate these things to the known particles and the standard model, etc. Very interesting stuff.